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Show by a numerical example and geometrically also that ` vec axx vec b= vec axx vec c` does not imply ` vec b= vec c`

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If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,

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CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. The position vectors of the vertices of a quadrilateral with A as o...

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  2. If vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , t...

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  3. Show by a numerical example and geometrically also that vec axx ve...

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  4. In triangle A B C ,points D , Ea n dF are taken on the sides B C ,C Aa...

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  5. Let A ,B ,C be points with position vectors 2 hat i- hat j+ hat k , ...

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  6. Let vec a and vec b be unit vectors such that | vec a+ vec b|=sqrt(3)...

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  7. If u and v are two non-collinear unit vectors such that |vecu...

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  8. A rigid body is spinning about a fixed point (3,-2,-1) with an angu...

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  9. vec rxx vec a= vec bxx vec a ; vec rxx vec b= vec axx vec b ; vec a!= ...

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  10. If | vec a|=2, then find the value of | vec axx hat i|^2+| vec axx hat...

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  11. If veca , vecb , vecc are position vectors of the vertices A, ...

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  12. A , B , Ca n dD are any four points in the space, then prove that | ...

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  13. Find the area of the parallelogram whose adjacent sides are determin...

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  14. Using vectors, find the area of the triangle with vertices A (1, 1,...

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  15. Let vec a , vec ba n d vec c be three verctors such that vec a!=0...

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  16. Find the area of a parallelogram whose diagonals are vec a=3 hat i+...

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  17. If vec a and vec b are unit vectors such that ( vec a+ vec b).[(2 ve...

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  18. If vec aa n d vec b are any two unit vectors, then find the greate...

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  19. If the vectors vec a , vec b ,a n d vec c form the sidesB C ,C Aa n d...

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  20. Let vec u be a vector on rectangular coordinate system with slopin...

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